A superconducting critical temperature above 200 K has recently been discovered in H2S (or D2S) under high hydrostatic pressure1,2. These measurements were interpreted in terms of a decomposition of these materials into elemental sulfur and a hydrogen-rich hydride that is responsible for the superconductivity, although direct experimental evidence for this mechanism has so far been lacking. Here we report the crystal structure of the superconducting phase of hydrogen sulfide (and deuterium sulfide) in the normal and superconducting states obtained by means of synchrotron X-ray diffraction measurements, combined with electrical resistance measurements at both room and low temperatures. We find that the superconducting phase is mostly in good agreement with the theoretically predicted body-centred cubic (bcc) structure for H3S3. The presence of elemental sulfur is also manifest in the X-ray diffraction patterns, thus proving the decomposition mechanism of H2S to H3S + S under pressure4,5,6.
Recently, a very high Tc of 200 K has been discovered in the hydrogen sulfide system1,2. This work was initiated by the prediction of a substantial superconductivity in H2S (ref. 7), which in turn arises from the idea that hydrogen-dominant metallic alloys might be superconductors with high critical temperature, similar to pure metallic hydrogen8.
The superconducting transition was proved by the sharp drop of the resistance to zero, a strong isotope effect in a study of D2S, a shift of the superconducting transition with magnetic field, and finally by measuring the magnetic susceptibility and magnetization. As a likely explanation, the authors1,2 suggested that H2S decomposes under pressure (with the assistance of temperature) to pure sulfur and some sulfur hydride with a higher content of hydrogen (such as SH4 or similar). At the same time, a theoretical work appeared which considered a different starting material (H2S)2H2 (stoichiometry H3S) and found R3m and Im-3m structures under pressure above 111 GPa and 180 GPa, respectively3. These structures and other stoichiometric compounds were further carefully studied theoretically by different groups in numerous works4,6,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25 and Tc ∼ 200 K was consistently obtained for the Im-3m structure. The calculated Tc, as well as its pressure dependence9, are close to the experimental data1,2. This suggests that the high Tc observed in the experiments relates not to H2S, but to the H3S in the Im-3m structure. Later calculations supported this idea: H2S is indeed unstable at high pressures and should decompose to sulfur and higher hydrides, most likely to H3S4,6,12. The goal of the present work is to check experimentally the structure of the superconducting hydrogen sulfide and compare it with the theoretically predicted structure.
Samples were prepared in the same way as described in refs 1,2—H2S was loaded at temperatures of ∼200 K, then the pressure was increased to ∼150–170 GPa and the sample was annealed at room temperature. Typical X-ray diffraction (XRD) images of sulfur hydride and sulfur deuteride pressurized to 150–173 GPa are shown in Fig. 1. The XRD patterns of sulfur hydride and sulfur deuteride samples do not differ from each other. The diffraction patterns seem to be produced by two major phases. This clearly follows from the different pressure dependence of the peaks (Fig. 2 and Supplementary Fig. 3) and different variation of intensities while scanning the sample over its diameter (Supplementary Fig. 1): one group is fitted by elemental sulfur of the β-Po structure26 and another group is described by the bcc structure of H3S from the theoretical work3. We can conclude that H2S (D2S) solid most likely decomposes under pressure via the route: 3H2S → 2H3S + S.
The pressure dependence of the atomic volume, Vatm, of sulfur hydride and sulfur deuteride are shown in Fig. 2c. It is fitted by a first-order Birch equation of state27 with the bulk modulus B0 = 506 (30) GPa, and its pressure derivative B0′ = 6 (fixed). The value of the experimentally observed Vatm is slightly larger, but the compressibility is in good agreement with Duan’s calculation3. The pressure dependence of the normalized atomic volume V/V0 of elemental sulfur in the β-Po structure is shown in Supplementary Fig. 3. It is in a good agreement with the experimental data of ref. 26 at high pressures P > 170 GPa, and with our density functional theory calculations (see Methods).
Our powder XRD measurements do not allow us to distinguish between the predicted bcc structures: Im-3m and R3m. In these structures the positions of the sulfur atoms are the same and the only difference is the position of the hydrogen atoms: hydrogen atoms are situated symmetrically between neighbouring sulfur atoms in the Im-3m structure and slightly asymmetrically in the R3m structure (Supplementary Fig. 2). However, the position of the hydrogen atoms cannot be determined from the powder measurements, as hydrogen atoms are extremely weak scatterers.
The low-temperature data help with further analysis. We measured simultaneously the XRD and electrical resistance in the same set-up28 (Fig. 3). The transition to the superconducting state was determined from the sharp drop of the resistance (Fig. 3a, b). We found that the normal and the superconducting state have the same structure, as the XRD patterns are the same at room and low temperatures (Fig. 1d). Moreover, the structure of the sample does not change visibly over the pressure range 92–173 GPa. This is in a contrast to the dependence of the critical temperature on pressure, which has a pronounced kink at 150 GPa for H3S and 160 GPa for D3S (Fig. 3c). This kink finds a natural explanation in the theoretical predictions9,23: the pressure dependence of the critical superconducting temperature is different in the R3m phase at lower pressures and in the Im-3m phase at higher pressures. Our XRD measurements support this interpretation, as R3m and Im-3m phases differ only in the ordering of the hydrogen atoms, and the same XRD patterns should be the same in the both pressure domains. Thus, one can conclude that the highest critical temperature of 203 K (ref. 2) corresponds to the Im-3m phase.
The sample and electrical probes were prepared by similar method to ref. 2. Angle-dispersive powder XRD measurements were carried out at SPring-8 (beamline BL10XU) with a monochromatic beam of energy ∼30.0 keV (λ ∼ 0.412–0.414 Å). XRD and electrical resistance were measured simultaneously with the aid of a cryostat28. The diffraction patterns were recorded using an imaging plate with an exposure time between 120 and 300 s. Four-probe electrical measurements were performed with an a.c.-resistance bridge (Linear Research, LR-700). We determined the pressure–volume dependence of β-Po sulfur by means of first-principles calculations based on density functional theory. The Quantum ESPRESSO code29 was used for the calculations, in which the Perdew–Burke–Ernzerhof generalized gradient approximation30 and the Vanderbilt ultrasoft pseudopotential31 were employed. The k-space integration over the Brillouin zone was performed on a 24 × 24 × 24 grid, and the energy cutoff of the plane wave basis was set at 80 Ry.
Raw data were generated at the SPring-8 synchrotron radiation facility (beamline BL10XU). Derived data supporting the findings of this study are available from the corresponding author on request.
This work was performed under proposal No. 2015A0112 of the SPring-8. This research was supported by Japan Society for the Promotion of Science Grant-in-Aid for Specially Promoted Research, No. 26000006, JSPS KAKENHI, Grant-in-Aid for Young Scientists (B), No.15K17707 and the European Research Council 2010-Advanced Grant 267777.
About this article
Quantum Studies: Mathematics and Foundations (2018)